Question 1171718: Ben and Peter start off together on a 24 km hike. Ben walks twice as fast as Peter, and when he comes to the end of the hike he turns around and walks back to meet Peter. How far, in km, has Peter walked when they meet?
Answer by ikleyn(52792)   (Show Source):
You can put this solution on YOUR website! .
When Ben will reach the end of the hike, Peter will be at the mid of the hike distance.
In other word, when Ben is at the point with coordinate 24 kilometers from the starting point, Peter is only
at 12 kilometers distance from the starting point.
Now Ben turns and goes back to meet Peter; Peter continue his way from that mid point.
At this moment, the distance between them is 24-12 = 12 kilometers.
Since Ben walks twice as fast as Peter, they will meet at the point, which separate these 12 kilometers
distance in ratio 2:1.
It means that the meeting point is at 4 km distance from the midpoint in direction to the end of the hike.
ANSWER. They meet each other at the point, which is 12+4 = 16 kilometers away from the starting point.
Solved.
So, this problem admits simple mental solution.
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